Difference between revisions of "Subgroup"
From Online Dictionary of Crystallography
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*[[Coset]] | *[[Coset]] | ||
*[[Normal subgroup]] | *[[Normal subgroup]] | ||
| + | *[[Supergroup]] | ||
*Section 8.3.3 in the ''International Tables for Crystallography, Volume A'' | *Section 8.3.3 in the ''International Tables for Crystallography, Volume A'' | ||
[[Category:Fundamental crystallography]] | [[Category:Fundamental crystallography]] | ||
Revision as of 08:27, 30 June 2008
Sous-groupe (Fr); Untergruppe (Ge); Subgrupo (Sp); Sottogruppo (It); 部分群 (Ja).
Let G be a group and H a non-empty subset of G. Then H is called a subgroup of H if the elements of H obey the group postulates.
The subgroup H is called a proper subgroup of G if there are elements of G not contained in H.
A subgroup H of G is called a maximal subgroup of G if there is no proper subgroup M of G such that H is a proper subgroup of M.
See also
- Complex
- Coset
- Normal subgroup
- Supergroup
- Section 8.3.3 in the International Tables for Crystallography, Volume A